## Monday, June 14, 2010

### Give Me A Lift

A couple of weeks ago, I had a mishap with the lawn tractor which rendered it unserviceable.

I still don't know exactly what's wrong with it, but I do know the mowing deck lift mechanism is damaged. It now has two positions: all the way up, or all the way down. Such is the way when you hit a tree root.

In a let's-pass-the-bill-to-find-out-what's-in-it fashion, I bought a tractor lift so I can find out just what is ailing my mower. It's just simple physics, really - a giant lever to lift the front end up so you can look underneath. It just helps that this lever is a tempered steel construction.

[WP] The magnitude of torque depends on three quantities: First, the force applied; second, the length of the lever arm[4] connecting the axis to the point of force application; and third, the angle between the two. In symbols:

$\boldsymbol \tau = \mathbf{r}\times \mathbf{F}\,\!$
$\tau = rF\sin \theta\,\!$

where

τ is the torque vector and τ is the magnitude of the torque,
r is the displacement vector (a vector from the point from which torque is measured to the point where force is applied), and r is the length (or magnitude) of the lever arm vector,
F is the force vector, and F is the magnitude of the force,
× denotes the cross product,
θ is the angle between the force vector and the lever arm vector.

The length of the lever arm is particularly important; choosing this length appropriately lies behind the operation of levers, pulleys, gears, and most other simple machines involving a mechanical advantage.

I put it together tonight and can't wait to use it. It is a very manly activity (grunt, grunt). Everybody should have a tractor and a lift to go with it.

Not to be outdone, however, Blynken came out from her bed tonight and wanted to know what "that smell" was.

"It smells like the lawn mower."

"It is the lawn mower - or at least a lawn tractor lift.", I said. "It smells like industrial grade metal, plastic, and rubber."

Whatever.